Name That Permutation

The concept of permutations comes up frequently in the
analysis of computer algorithms, in probability theory, and in
many other fields. For many algorithmic problems, the easiest
brute-force-type solution is to enumerate all possible
permutations of some list or set, and test each permutation to
see if it provides the correct solution. One problems which is
easy to view this way is the classic traveling salesman
problem. This is not to suggest that enumerating all
permutations is the most efficient solution method!

For this problem, write a program that takes a list of
unique numbers from $1$ to
$n$ and produces the
$k$th permutation of that
list. The first permutation ($k=0$) is the list in sorted order,
i.e. $1, 2, 3, \ldots ,
n$. The last permutation ($k=n!-1$) is the list in reverse
sorted order. The progression of permutations follows the
standard numeric sorting rules. So for $n=4$, the following are the order of
permutations, from $k=0$
to $k=4!-1=23$:

$k$

permutation

$k$

permutation

$k$

permutation

$k$

permutation

$0$

$1~ 2~ 3~
4$

$6$

$2~ 1~ 3~
4$

$12$

$3~ 1~ 2~
4$

$18$

$4~ 1~ 2~
3$

$1$

$1~ 2~ 4~
3$

$7$

$2~ 1~ 4~
3$

$13$

$3~ 1~ 4~
2$

$19$

$4~ 1~ 3~
2$

$2$

$1~ 3~ 2~
4$

$8$

$2~ 3~ 1~
4$

$14$

$3~ 2~ 1~
4$

$20$

$4~ 2~ 1~
3$

$3$

$1~ 3~ 4~
2$

$9$

$2~ 3~ 4~
1$

$15$

$3~ 2~ 4~
1$

$21$

$4~ 2~ 3~
1$

$4$

$1~ 4~ 2~
3$

$10$

$2~ 4~ 1~
3$

$16$

$3~ 4~ 1~
2$

$22$

$4~ 3~ 1~
2$

$5$

$1~ 4~ 3~
2$

$11$

$2~ 4~ 3~
1$

$17$

$3~ 4~ 2~
1$

$23$

$4~ 3~ 2~
1$

Input

Input consists of up to $1\,
000$ test cases, one per line. Each test case has two
integers $1 \leq n \leq
50$ and $0 \leq k \leq
n!-1$. Input ends at the end of file.

Output

For each test case, print a line containing the $k$th permutation of the numbers
$1$ through $n$.